.5.26.73.....5.2...2..4.5..6..57.329972.3685..358926.7...327465563.8.172247615983OK, taking it from here, let’s try a little translation. My solution could have been written more fully as:1r6c1 => 1r5c9,1r4c6 => 1r1c3 (1 is now excluded from all other cells in Row1)||4r6c1 => 4r5c9,4r4c6 => 4r1c3 (the same exclusions now apply for candidate 4)So r1c3 <> 9 => 9r1c6, stte. This could be read literally as meaning:“The only two possible candidates for r6c1 both predict that same candidate in r1c3.Therefore r1c3 cannot be 9 and so the 9 in Row1 must be at r1c6. This allows the remaining cells to be solved in singles.”I hadn’t noticed the exclusion of 8 at r1c3, as the definite placement of 9 at r1c6 solved the puzzle for me.SpAce described the eliminations in a chain (not sure about * and ^)(1)r6c1* - r6c8 = r5c9^ - r5c4 = r4c6 - r1c6*1^9 = (1)r1c3||(4)r6c1* - r6c8 = r5c9 - r1c9*1 = (4)r1c3=> -89 r1c3; stte. Is it possible to read this chain as a statement in English which tells the same story?

Almost. The latter implications are not independently correct as written because they depend on the original premise. Also, 4r4c6 is irrelevant so it should not be listed. If you insist on using the forcing chain style, I'd write it like this:

Either way, I personally think that style is hard to follow, because it jumps over the negation steps (and often others too, as in here as well).

I hadn’t noticed the exclusion of 8 at r1c3, as the definite placement of 9 at r1c6 solved the puzzle for me.

You're right that it's not necessary for the solution, but it's a good practice to list all eliminations following from a piece of logic. It wouldn't show in your style which has a placement as the final conclusion.

SpAce described the eliminations in a chain (not sure about * and ^)

They're memory markers and necessary here because the chains aren't linear (they branch, which makes them nets). I used one in my own (first) solution too. The markers are there basically for the same reason why the original premise had to be repeated in your forcing chain to make the logic work as intended.

Yes, but I don't like such plain English statements because they're long, hard to follow, and often ambiguous. Chains and nets describe the logic more concisely and accurately. Here's the same thing using a full net diagram: